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Simplifying 9(x + -6) * x = 14 Reorder the terms: 9(-6 + x) * x = 14 Reorder the terms for easier multiplication: 9x(-6 + x) = 14 (-6 * 9x + x * 9x) = 14 (-54x + 9x2) = 14 Solving -54x + 9x2 = 14 Solving for variable 'x'. Reorder the terms: -14 + -54x + 9x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + -54x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.555555556 + -6x + x2 = 0 Move the constant term to the right: Add '1.555555556' to each side of the equation. -1.555555556 + -6x + 1.555555556 + x2 = 0 + 1.555555556 Reorder the terms: -1.555555556 + 1.555555556 + -6x + x2 = 0 + 1.555555556 Combine like terms: -1.555555556 + 1.555555556 = 0.000000000 0.000000000 + -6x + x2 = 0 + 1.555555556 -6x + x2 = 0 + 1.555555556 Combine like terms: 0 + 1.555555556 = 1.555555556 -6x + x2 = 1.555555556 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 1.555555556 + 9 Reorder the terms: 9 + -6x + x2 = 1.555555556 + 9 Combine like terms: 1.555555556 + 9 = 10.555555556 9 + -6x + x2 = 10.555555556 Factor a perfect square on the left side: (x + -3)(x + -3) = 10.555555556 Calculate the square root of the right side: 3.248931448 Break this problem into two subproblems by setting (x + -3) equal to 3.248931448 and -3.248931448.Subproblem 1
x + -3 = 3.248931448 Simplifying x + -3 = 3.248931448 Reorder the terms: -3 + x = 3.248931448 Solving -3 + x = 3.248931448 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.248931448 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.248931448 + 3 x = 3.248931448 + 3 Combine like terms: 3.248931448 + 3 = 6.248931448 x = 6.248931448 Simplifying x = 6.248931448Subproblem 2
x + -3 = -3.248931448 Simplifying x + -3 = -3.248931448 Reorder the terms: -3 + x = -3.248931448 Solving -3 + x = -3.248931448 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.248931448 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.248931448 + 3 x = -3.248931448 + 3 Combine like terms: -3.248931448 + 3 = -0.248931448 x = -0.248931448 Simplifying x = -0.248931448Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.248931448, -0.248931448}
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